# Sampling-based Safe Reinforcement Learning for Nonlinear Dynamical Systems

arXiv: https://arxiv.org/abs/2403.04007 · HTML: https://mlsanity.com/paper/2403.04007/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Safe and constrained RL, one of 15 directions in Deep reinforcement learning methods.
- Builds on 20 of its 57 references that are in the map.
- First posted on arXiv 6 Mar 2024.

## Placed in

- Deep reinforcement learning methods / [Safe and constrained RL](https://mlsanity.com/deeprl/safe-and-constrained-rl/)

## Builds on (most cited first, 20 of 20)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [On the Theory of Policy Gradient Methods: Optimality, Approximation, and Distribution Shift](https://mlsanity.com/paper/1908.00261/) (2019)
- [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017)
- [Constrained Reinforcement Learning Has Zero Duality Gap](https://mlsanity.com/paper/1910.13393/) (2019)
- [Global Convergence of Policy Gradient Methods to (Almost) Locally Optimal Policies](https://mlsanity.com/paper/1906.08383/) (2019)
- [Achieving Zero Constraint Violation for Constrained Reinforcement Learning via Primal-Dual Approach](https://mlsanity.com/paper/2109.06332/) (2021)
- [Policy Optimization for H2 Linear Control with H_∞ Robustness Guarantee: Implicit Regularization and Global Convergence](https://mlsanity.com/paper/1910.09496/) (2019)
- [Model-based Constrained Reinforcement Learning using Generalized Control Barrier Function](https://mlsanity.com/paper/2103.01556/) (2021)
- [Beyond Exponentially Fast Mixing in Average-Reward Reinforcement Learning via Multi-Level Monte Carlo Actor-Critic](https://mlsanity.com/paper/2301.12083/) (2023)
- [Reinforcement Learning based Distributed Control of Dissipative Networked Systems](https://mlsanity.com/paper/2011.14263/) (2020)

## Built on by (most cited first, 4 of 4)

- [Anytime Safe Reinforcement Learning](https://mlsanity.com/paper/2504.16417/) (2025)
- [Off-Policy Reinforcement Learning with Anytime Safety Guarantees via Robust Safe Gradient Flow](https://mlsanity.com/paper/2510.01492/) (2025)
- [Safe Online Learning via Smooth Safety-Structured Policy Composition](https://mlsanity.com/paper/2606.31320/) (2026)
- [SafePG: Safe and Globally Optimal Reinforcement Learning with Hard Constraints](https://mlsanity.com/paper/2609.14076/) (2026)

## Abstract (arXiv)

We develop provably safe and convergent reinforcement learning (RL) algorithms for control of nonlinear dynamical systems, bridging the gap between the hard safety guarantees of control theory and the convergence guarantees of RL theory. Recent advances at the intersection of control and RL follow a two-stage, safety filter approach to enforcing hard safety constraints: model-free RL is used to learn a potentially unsafe controller, whose actions are projected onto safe sets prescribed, for example, by a control barrier function. Though safe, such approaches lose any convergence guarantees enjoyed by the underlying RL methods. In this paper, we develop a single-stage, sampling-based approach to hard constraint satisfaction that learns RL controllers enjoying classical convergence guarantees while satisfying hard safety constraints throughout training and deployment. We validate the efficacy of our approach in simulation, including safe control of a quadcopter in a challenging obstacle avoidance problem, and demonstrate that it outperforms existing benchmarks.